Extended trees of graphs. (English) Zbl 0814.05027

The paper introduces the concept of an extended tree of a graph in the following way: Let \(G\) be a finite connected graph. If \(G\) is a tree, then the unique extended tree of \(G\) is \(G\) itself. If not, then \(G\) contains a circuit and thus there exists a vertex \(v\) on the circuit and a partition of the set of edges incident with \(v\) such that the vertex splitting in \(v\) according to the partition is not disconnecting. We perform the splitting according to one of the chosen two-element partitions. We repeat this procedure, until a tree is obtained. This tree is called an extended tree. The properties of these trees are studied.


05C05 Trees
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